text: It is also possible to mathematically express the Peregrine soliton according to the spatial frequency :
  with  being the Dirac delta function.
  This corresponds to a modulus (with the constant continuous background here omitted) :
  One can notice that for any given time , the modulus of the spectrum exhibits a typical triangular shape when plotted on a logarithmic scale. The broadest spectrum is obtained for , which corresponds to the maximum of compression of the spatio-temporal nonlinear structure.